Let's start with the basics. Here are 5 straightforward tips to help you communicate effectively with data.
1. Keep your audience in mind. You are creating a data visualization because you want to communicate something to someone; keep that someone top of mind throughout the design process. Use visual cues (size, color, placement on page) to help direct your audience's eye and provide signals on what to pay attention to. Easy test: show your visual to a colleague who has limited context and let them tell you how they process the information (where they focus, what observations they make) - this is a good proxy for your audience, so if they aren't paying attention to the right things, revisit the design.
2. Choose display based on what you want to show. Let the question you are trying to answer determine the appropriate chart type. The correct answer to the question "what is the right chart type?" is always the same: whatever will be the easiest for your audience to interpret. Don't shy away from bar charts because they are common: use them because they are common - this means less of a learning curve for your audience to understand the information that you are providing.
3. Aim for simplicity. A complicated-looking visual can turn off an audience, as it means it will likely take time to get at the information that's being provided. Don't make your audience work to get the information - as the designer, you should take that work upon yourself to make the message clear. Strip out anything that doesn't have informative value - every step in reduction makes what remains stand out more. Don't be afraid of white space. Preserve margins (if you're unable to do this and have already eliminated the nonessential, you should think about breaking the message into multiple pieces so as not to overwhelm). Simple is better than complicated.
4. Support with text. Every chart needs a title, every axis needs a label - no exceptions! As the designer of the visual, you are more familiar with the content than your audience; help them understand the information by explaining the unfamiliar, citing data sources and as of date, and outlining methodology as warranted. The best place to put text is a close as possible to what it's describing, so long as it doesn't obscure the information. If you want your audience to draw a specific conclusion, state it explicitly.
5. Use color strategically. The use of color should always be an explicit decision. Use color sparingly and strategically to highlight the important parts of your visual: color is a strong visual cue to help your audience understand where they should focus their attention. In general, aim to use a color palette of shades of grey with pointed use of color. Around 10% of people are colorblind, which typically means difficulty distinguishing between shades of red and shades of green, so keep this in mind in your design.